CMSC 679: Theory of Computation


Instructor: 	Howard E. Motteler
Office: 	TF 111
Phone: 		455-2590
Office hours: 	before class

Text:  Lewis & Papadimitriou.  Readings from others, 
including Rodgers and Machtey & Young.

Grading:  2 midterms and a final, one of which may be a take-home
exam.  Exercises will periodically be given, and it is strongly
reccomended that you do these, although they are not graded.
Solutions will (usually) be given.  The weighting of the exams is
100 pts for each midterm, and 150 pts for the final, for a total 
of 350.

Topics:

* Introduction to Computability

Church's Thesis and Effective Computability
Primitive recursive functions

* Basic Recursive Function Theory

Recursive functions.  S1-1 functions, composition functions, 
universal functions.  Acceptable programming systems. 
Recursion theorems.  Rice's theorem and some extensions to 
Rices's theorem.  Recursive and RE sets.  Reducability.  
Roger's isomorphism theorem.  The arithmetic hierarchy.

* Turing machines and other models of computation

Turing machines, markov algorithms, RAM models, and recursive
functions are all shown to be equivalent.

* Complexity theory and NP-completeness

Introduction to time and space measures. "hard" and 
"complete" problems.  Cook's theorem, NP-completeness.
Survey of some common NP-complete problems.

* Logic

Propositional logic.  Truth assignments, tautologies, logical
consequence.  Resolution, compactness.  Introduction to first 
order logic:  well formed formulas, rules of inference, models.
Compactness and completeness.